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2. Graph theory - Wikipedia

   en.wikipedia.org/wiki/Graph_theory

   A drawing of a graph. In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of vertices (also called nodes or points) which are connected by edges (also called arcs, links or lines ).

3. Shortest path problem - Wikipedia

   en.wikipedia.org/wiki/Shortest_path_problem

   In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. The problem of finding the shortest path between two intersections on a road map may be modeled as a special case of the shortest path problem in graphs ...

4. List of NP-complete problems - Wikipedia

   en.wikipedia.org/wiki/List_of_NP-complete_problems

   The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3] : . ND22, ND23. Vehicle routing problem.

5. Hamiltonian path problem - Wikipedia

   en.wikipedia.org/wiki/Hamiltonian_path_problem

   The Hamiltonian path problem is a topic discussed in the fields of complexity theory and graph theory. It decides if a directed or undirected graph, G, contains a Hamiltonian path, a path that visits every vertex in the graph exactly once. The problem may specify the start and end of the path, in which case the starting vertex s and ending ...

6. Graph coloring - Wikipedia

   en.wikipedia.org/wiki/Graph_coloring

   Graph coloring. A proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible. In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints. In its simplest form, it is a way of coloring the ...

7. Directed acyclic graph - Wikipedia

   en.wikipedia.org/wiki/Directed_acyclic_graph

   In mathematics, particularly graph theory, and computer science, a directed acyclic graph ( DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs ), with each edge directed from one vertex to another, such that following those directions will never form a closed loop.

8. Steiner tree problem - Wikipedia

   en.wikipedia.org/wiki/Steiner_tree_problem

   Steiner tree problems in graphs are applied to various problems in research and industry, including multicast routing and bioinformatics. A special case of this problem is when G is a complete graph, each vertex v ∈ V corresponds to a point in a metric space, and the edge weights w(e) for each e ∈ E correspond to distances in the space.

9. Tree (graph theory) - Wikipedia

   en.wikipedia.org/wiki/Tree_(graph_theory)

   v − 1. Chromatic number. 2 if v > 1. Table of graphs and parameters. In graph theory, a tree is an undirected graph in which any two vertices are connected by exactly one path, or equivalently a connected acyclic undirected graph. [ 1] A forest is an undirected graph in which any two vertices are connected by at most one path, or equivalently ...